magnetochemistry

Article

Torque-Detected Electron Spin Resonance as a Toolto Investigate Magnetic Anisotropyin Molecular Nanomagnets

María Dörfel 1, Michal Kern 1, Heiko Bamberger 1, Petr Neugebauer 1, Katharina Bader 1,Raphael Marx 1, Andrea Cornia 2, Tamoghna Mitra 3, Achim Müller 3, Martin Dressel 4,Lapo Bogani 4,† and Joris van Slageren 1,*

1 Institut für Physikalische Chemie, Universität Stuttgart, Pfaffenwaldring 55, 70569 Stuttgart, Germany;mariadorfel@gmail.com (M.D.); m.kern@ipc.uni-stuttgart.de (M.K.);heiko.bamberger@ipc.uni-stuttgart.de (H.B.); petr.neugebauer@ipc.uni-stuttgart.de (P.N.);katharina.bader@ipc.uni-stuttgart.de (K.B.); r.marx@ipc.uni-stuttgart.de (R.M.)

2 Department of Chemical and Geological Sciences & INSTM Research Unit,University of Modena and Reggio Emilia, via G. Campi 103, I-41125 Modena, Italy;andrea.cornia@unimore.it

3 Fakultät für Chemie, Universität Bielefeld, 33501 Bielefeld, Germany; tamoghnamitra@yahoo.co.in (T.M.);a.mueller@uni-bielefeld.de (A.M.)

4 Physikalisches Institut, Universität Stuttgart, Pfaffenwaldring 57, 70569 Stuttgart, Germany;dressel@pi1.physik.uni-stuttgart.de (M.D.); lapo.bogani@materials.ox.ac.uk (L.B.)

* Correspondence: slageren@ipc.uni-stuttgart.de; Tel.: +49-711-6856-4380† Present address: Department of Materials, University of Oxford, 16 Parks Road, Oxford OX1 3PH, UK.

Academic Editors: Marius Andruh and Liviu F. ChibotaruReceived: 4 March 2016; Accepted: 26 April 2016; Published: 6 May 2016

Abstract: The method of choice for in-depth investigation of the magnetic anisotropy in molecularnanomagnets is high-frequency electron spin resonance (HFESR) spectroscopy. It has the benefits ofhigh resolution and facile access to large energy splittings. However, the sensitivity is limited to about107 spins for a reasonable data acquisition time. In contrast, methods based on the measurement ofthe deflection of a cantilever were shown to enable single spin magnetic resonance sensitivity. In thearea of molecular nanomagnets, the technique of torque detected electron spin resonance (TDESR)has been used sporadically. Here, we explore the applicability of that technique by investigatingmolecular nanomagnets with different types of magnetic anisotropy. We also assess different methodsfor the detection of the magnetic torque. We find that all types of samples are amenable to thesestudies, but that sensitivities do not yet rival those of HFESR.

Keywords: magnetic resonance; molecular nanomagnet; magnetic anisotropy

1. Introduction

Molecular nanomagnets (MNMs) are mono- or polynuclear complexes of p-, d- and/or f-blockelements [1]. MNMs can possess a range of interesting properties, including slow relaxation ofthe magnetic moment, quantum tunneling, magnetocaloric effects, and quantum coherence [2–5].The first of these properties originates from magnetic anisotropy, which causes the magnetic responseof the system to depend on the orientation of an applied magnetic field in the molecular coordinateframe. Under favorable circumstances, such an orientation dependence can engender an energy barrierbetween the up- and down-orientations of the magnetic moment. Magnetic anisotropy manifestsitself in a range of magnetic interactions, including the Zeeman interaction (g-value anisotropy),the exchange interaction (anisotropic and antisymmetric exchange), zero-field splitting (in ions withoutfirst-order orbital angular momentum) and crystal field splitting (in f-elements).

Magnetochemistry 2016, 2, 25; doi:10.3390/magnetochemistry2020025 www.mdpi.com/journal/magnetochemistry

Magnetochemistry 2016, 2, 25 2 of 9

Magnetic anisotropy can be investigated by several experimental techniques, such asmagnetometry [6,7], far-infrared spectroscopy [8,9], neutron scattering [10,11], and specific heatmeasurements [12]. However, probably the most popular method is that of high-frequency electronspin resonance (HFESR) spectroscopy. It delivers high g-value-resolution, especially important forbiological systems [13]. Importantly for the subject of this article, it allows experimental access tolarge energy splittings, such as those associated with magnetic anisotropy in MNMs [14]. It hasalso been used for the determination of anisotropic exchange interactions [15]. Finally, it canbe operated in field and frequency domains [16]. However, the ultimate sensitivity of HFESRtechniques, where the transmission or reflection of microwave photons is detected, is likely to beworse than a million spins. Indeed, the direct detection of microwave photons is an intrinsicallylow-sensitivity method, as microwave photons carry very small energies compared to, for instance,photons in the visible range. With the drive of the field to investigate (sub)monolayers of MNMsfor applications in spintronic devices [17,18] this sensitivity is not sufficient. Alternative electronspin resonance (ESR) detection methods include those where the change in magnetization dueto magnetic resonance is measured by superconducting interference device (SQUID) or Hall barsensors [19]. Some of us as well as others have developed the technique of torque-detected electronspin resonance (TDESR) spectroscopy for the investigation of molecular nanomagnets [20–22]. Thistechnique relies on the effect of magnetic resonance on magnetic torque τ = M ˆ B and hence onthe deflection of a cantilever on which the sample is mounted. This deflection is measured byrecording the change in capacitance between the cantilever arm and a parallel plate (cantilevertorque magnetometry, CTM). In other systems, cantilever-detected electron spin resonance wasshown to reach single spin sensitivity [23]. For this method to work, the presence of magneticanisotropy is essential to ensure noncollinearity of the magnetization M and the magnetic fieldB [24]. The frequency resolution is given by the monochromaticity of the source, which is inthe 101 MHz range. The field resolution depends on the field homogeneity, which is 0.1% overone cm radius, corresponding to 10 G in a 1 T field. However, typical samples used here areof mm size, and, in practice, the field resolution is better than 1 G. Thus far, our investigationswere limited to a single sample with a large zero-field splitting, namely [Fe4(L)2(dpm)6] (Fe4)where Hdpm is 2,2,6,6-tetramethyl-3,5-heptanedione (also known as dipivaloylmethane) and H3Lis (R,S)-2-hydroxymethyl-2-(2-methyl-butoxymethyl)propane-1,3-diol [20,21]. It is now essential toestablish the ability of the technique to probe other sources of magnetic anisotropy, as well as to explorealternative detection methods.

Here, we present new TDESR results, where we exploit optical rather than capacitivedetection of cantilever deflection. In addition, we expand the range of investigated samples toinclude [Mn12O12(OAc)16(H2O)4]¨ 2AcOH¨ 4H2O (Mn12Ac), K6[V15As6O42(H2O)]¨ 8H2O (V15) and(PPh4-d20)2[Cu(mnt)2] (Cu-mnt), where H2mnt is maleonitriledithiol. In these samples, the magneticanisotropy originates from zero-field splitting, antisymmetric exchange interactions and g-valueanisotropy, respectively.

2. Results

Previous TDESR measurements [20,21,25] relied on capacitive detection of cantilever deflectiondue to magnetic torque (capacitively-detected (CD-)TDESR). To this end the capacitance betweenthe CuBe cantilever (on which the sample is mounted) and a copper bottom plate is measured(Figure 1a). The cantilever is mounted on a movable sample holder, allowing for sliding between theaperture position, for alignment of the microwave source (100–1000 GHz), and the cantilever positionfor measurement. This setup was rather sensitive to electronic noise. Measurement of cantileverdeflection is also at the heart of atomic force microscopy methods, in which case the deflection isdetected by means of a laser beam reflected by the cantilever. Given that force microscopy methodsenable measurement of single spins [23], we have considered an alternative measurement setup [26].In this novel setup, the back plate of the cantilever sample holder is removed and the light spot of

Magnetochemistry 2016, 2, 25 3 of 9

a laser external to the optical cryomagnet is focused on the back of the cantilever. The shift in thereflected laser spot, determined by a position-sensitive detector (PSD), is a direct measure of cantileverdeflection (optically-detected (OD-)TDESR), Figure 1b). Figure 1c (top panel) shows the measuredshift as a function of the applied field under microwave irradiation at a constant frequency of 190 GHz(field-sweep TDESR), recorded on a single crystal of Fe4. The broad background is due to the fielddependence of the magnetic torque, which is typical for systems with large zero-field splittings [27].The sharp peaks are due to magnetic resonance transitions within the S = 5 ground spin multiplet ofthe molecule. By fitting the broad background with a spline, the magnetic resonance lines can be seenmore clearly (Figure 1c, bottom panel). As for traditional ESR, the line intensities in TDESR are relative,not absolute. The TDESR line intensity is a function of sample amount, of radiation intensity, of thesize of the radiation focus, of the spin-lattice relaxation rate and of the thermal coupling to the heatbath [28]. Quantitative simulation of the line intensities would require in-depth investigation of thesefactors, a task well beyond the scope of the present study. These results show a similar signal-to-noiseratio compared with previous data obtained by capacitive detection [25]. Considering the size of thesamples and the achieved signal-to-noise ratios, we estimate that the minimum number of spins thatcan be detected on the order of 1012. Sensitivity is thus several orders of magnitude worse than in thecase of HFESR.

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measured shift as a function of the applied field under microwave irradiation at a constant frequency 

of 190 GHz (field‐sweep TDESR), recorded on a single crystal of Fe4. The broad background is due to 

the  field  dependence  of  the magnetic  torque, which  is  typical  for  systems with  large  zero‐field 

splittings [27]. The sharp peaks are due to magnetic resonance transitions within the S = 5 ground 

spin multiplet of the molecule. By fitting the broad background with a spline, the magnetic resonance 

lines can be seen more clearly (Figure 1c, bottom panel). As for traditional ESR, the line intensities in 

TDESR  are  relative,  not  absolute.  The  TDESR  line  intensity  is  a  function  of  sample  amount,  of 

radiation  intensity, of  the size of  the  radiation  focus, of  the spin‐lattice  relaxation  rate and of  the 

thermal coupling to the heat bath [28]. Quantitative simulation of the line intensities would require 

in‐depth investigation of these factors, a task well beyond the scope of the present study. These results 

show a similar signal‐to‐noise ratio compared with previous data obtained by capacitive detection 

[25]. Considering the size of the samples and the achieved signal‐to‐noise ratios, we estimate that the 

minimum number of spins that can be detected on the order of 1012. Sensitivity is thus several orders 

of magnitude worse than in the case of HFESR. 

 

Figure 1. (a) schematic drawing of the bottom part of the sample rod, showing the sliding sample 

holder. This allows switching between an aperture for alignment purposes, and the cantilever (dark 

brown, with yellow bottom plate); (b) setup for optical detection of the cantilever deflection by means 

of  a  laser  and  position‐sensitive  detector  (PSD);  (c)  field‐domain  torque‐detected  electron  spin 

resonance (TDESR) measurements on a single crystal of Fe4 with the crystal c‐axis at 32° from the easy 

axis  and different  temperatures  as  indicated, with  raw  curves  on  top  and  the  baseline‐corrected 

spectra on the bottom. 

As a further test, we have focused on the archetypal single‐molecule magnet Mn12Ac, which has 

an S = 10 ground spin state. The magnetic properties in the ground state can be described well by 

means of the spin Hamiltonian: 

42 2 21

4B 430

( 1)q

qz x y

q

D S S S E S S B O

B g SH ,  (1)

where B is the magnetic field vector, g is the g matrix, D and E are the second‐rank axial and rhombic 

zero‐field splitting parameters, respectively, and Bq 

4  are the fourth‐rank zero‐field splitting parameters. 

The 2.5 × 0.5 × 0.5 mm3 crystal was oriented with its easy axis in the rotation plane (Figure S1) and 

both CD (Figure 2a) and OD (Figure 2b) frequency‐domain TDESR spectra were recorded at 7 K. CD‐

CTM measurements served to determine the exact orientation of the easy axis, exploiting the fact that 

the torque signal vanishes when the easy axis and the magnetic field are parallel. Note that in frequency‐

domain spectra, the field is kept constant and the torque signal without irradiation is thus also constant 

at each probed field value. The two sets of spectra display peaks in the region around 300 GHz and in 

the region around 250–260 GHz. These peaks, whose positions depend on the external field strength, 

Figure 1. (a) schematic drawing of the bottom part of the sample rod, showing the sliding sampleholder. This allows switching between an aperture for alignment purposes, and the cantilever (darkbrown, with yellow bottom plate); (b) setup for optical detection of the cantilever deflection by means ofa laser and position-sensitive detector (PSD); (c) field-domain torque-detected electron spin resonance(TDESR) measurements on a single crystal of Fe4 with the crystal c-axis at 32˝ from the easy axis anddifferent temperatures as indicated, with raw curves on top and the baseline-corrected spectra onthe bottom.

As a further test, we have focused on the archetypal single-molecule magnet Mn12Ac, which hasan S = 10 ground spin state. The magnetic properties in the ground state can be described well bymeans of the spin Hamiltonian:

H “ µBB ¨ g ¨ S`Dˆ

S2z ´

13

SpS` 1q˙

` E´

S2x ´ S2

y

¯

`

4ÿ

q“0

Bq4Oq

4, (1)

where B is the magnetic field vector, g is the g matrix, D and E are the second-rank axial and rhombiczero-field splitting parameters, respectively, and Bq

4 are the fourth-rank zero-field splitting parameters.

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The 2.5 ˆ 0.5 ˆ 0.5 mm3 crystal was oriented with its easy axis in the rotation plane (Figure S1)and both CD (Figure 2a) and OD (Figure 2b) frequency-domain TDESR spectra were recorded at 7 K.CD-CTM measurements served to determine the exact orientation of the easy axis, exploiting thefact that the torque signal vanishes when the easy axis and the magnetic field are parallel. Note thatin frequency-domain spectra, the field is kept constant and the torque signal without irradiation isthus also constant at each probed field value. The two sets of spectra display peaks in the regionaround 300 GHz and in the region around 250–260 GHz. These peaks, whose positions depend onthe external field strength, are attributed to magnetic resonance transitions from |MS = ˘ 10> to|˘9> and from |˘9> to |˘8>, respectively. The peaks in frequency-domain spectra have a muchmore ragged look than those in field-domain spectra, due to variations of the source intensity as afunction of frequency and due to standing waves in the radiation beam. The CD-TDESR spectracould be reproduced well by using published [29] spin Hamiltonian parameters g|| = 1.93, gK = 1.96,D = ´0.46 cm´1, B4 = ´2.2 ˆ 10´5 cm´1, |B4

4| = 4 ˆ 10´5 cm´1. The optically detected (OD-)TDESRspectra show essentially the same features, with differences in peak positions due to the differentangle between the c-axis and the magnetic field. The quality of the CD- and OD-TDESR spectra is verysimilar. OD-TDESR has the disadvantage that the rotation angle of the cantilever is limited by theaperture of the optical windows, and angle-dependent measurements are thus severely hampered.Therefore, in the following, we have focused on capacitively detected measurements only.

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are attributed  to magnetic resonance  transitions  from |MS = ± 10>  to |±9> and  from |±9>  to |±8>, 

respectively. The peaks in frequency‐domain spectra have a much more ragged look than those in 

field‐domain spectra, due to variations of the source intensity as a function of frequency and due to 

standing waves  in  the  radiation beam. The CD‐TDESR  spectra could be  reproduced well by using 

published [29] spin Hamiltonian parameters g‖ = 1.93, g = 1.96, D = −0.46 cm−1, B4 = −2.2 × 10−5 cm−1, 

|B44| = 4 × 10−5 cm−1. The optically detected (OD‐)TDESR spectra show essentially the same features, 

with differences  in peak positions due  to  the different angle between  the c‐axis and  the magnetic 

field. The quality of the CD‐ and OD‐TDESR spectra is very similar. OD‐TDESR has the disadvantage 

that the rotation angle of the cantilever is limited by the aperture of the optical windows, and angle‐

dependent measurements are thus severely hampered. Therefore, in the following, we have focused 

on capacitively detected measurements only. 

(a)  (b)

Figure 2. (a) capacitively detected frequency‐domain TDESR spectra recorded on a single crystal of 

Mn12Ac with the applied field 4° from the easy axis (c), at 7 K and different fields as indicated; (b) 

optically detected frequency‐domain TDESR spectra recorded on a single crystal of Mn12Ac with the 

crystal c‐axis 45° from the field, at 7 K and different fields as indicated. In both panels, solid lines are 

experimental data and dashed lines represent the simulations. 

The origin of magnetic anisotropy in Mn12Ac is the same as in Fe4, i.e., zero‐field splitting of the 

ground  spin  state. To explore  if other  sources of anisotropy also  suffice and allow  for  successful 

TDESR studies, we next focused on V15, which consists of fifteen S = ½ VO2+ ions [30]. Magnetically, 

this  compound has  a  layered  structure  consisting of  two  strongly  antiferromagnetically  coupled 

vanadyl hexagons (Figure S2). At the temperatures relevant to this studies, these hexagons can be 

considered diamagnetic. The  two hexagons sandwich  three  further vanadyl  ions, which are more 

weakly antiferromagnetically exchange coupled. In antiferromagnetically coupled equilateral S = ½ 

triangles, the ground manifold comprises two degenerate states with S = ½. In practice, a small energy 

gap is found between these two states. There has been a long debate on whether this splitting is due 

to the occurrence of antisymmetric exchange interactions or to an isosceles distortion of the triangle 

[31–34]. A suitable spin Hamiltonian for the description of the low temperature properties of V15 is: 

1 2 2 3 1 3 1 2 2 3 1 3BJ J B g S S S S S S S G S S S S S SH ,  (2)

where J′ and J are the isotropic exchange coupling constants (J′ = J for an equilateral triangle) and G 

is the antisymmetric exchange interaction vector. 

We have performed CTM measurements on a 1.0 × 0.5 × 0.5 mm3 single crystal of V15 (Figure 3a). 

The torque signal is much weaker for V15 compared to Mn12 for similar crystal sizes. For a satisfactory 

reproduction of CTM curves with a minimal model, it turns out that inclusion of the parameters g‖ = 

1.95, g = 1.98, J′ = J = 0.847 cm−1 and G = (0, 0, 0) suffices [35]. Hence, g value anisotropy is sufficient 

to observe a nonzero magnetic torque signal and CTM does not help distinguishing between the two 

aforementioned scenarios. It must be noted here that the cantilever torquemeter is not calibrated and 

Figure 2. (a) capacitively detected frequency-domain TDESR spectra recorded on a single crystalof Mn12Ac with the applied field 4˝ from the easy axis (c), at 7 K and different fields as indicated;(b) optically detected frequency-domain TDESR spectra recorded on a single crystal of Mn12Ac withthe crystal c-axis 45˝ from the field, at 7 K and different fields as indicated. In both panels, solid linesare experimental data and dashed lines represent the simulations.

The origin of magnetic anisotropy in Mn12Ac is the same as in Fe4, i.e., zero-field splitting ofthe ground spin state. To explore if other sources of anisotropy also suffice and allow for successfulTDESR studies, we next focused on V15, which consists of fifteen S = ½ VO2+ ions [30]. Magnetically,this compound has a layered structure consisting of two strongly antiferromagnetically coupledvanadyl hexagons (Figure S2). At the temperatures relevant to this studies, these hexagons canbe considered diamagnetic. The two hexagons sandwich three further vanadyl ions, which aremore weakly antiferromagnetically exchange coupled. In antiferromagnetically coupled equilateralS = ½ triangles, the ground manifold comprises two degenerate states with S = ½. In practice, a smallenergy gap is found between these two states. There has been a long debate on whether this splittingis due to the occurrence of antisymmetric exchange interactions or to an isosceles distortion of the

Magnetochemistry 2016, 2, 25 5 of 9

triangle [31–34]. A suitable spin Hamiltonian for the description of the low temperature properties ofV15 is:

H “ µBB ¨ g ¨ S` J1 S1 ¨ S2 ` J`

S2 ¨ S3 ` S1 ¨ S3˘

`G ¨`

S1 ˆ S2 ` S2 ˆ S3 ` S1 ˆ S3˘

, (2)

where J1 and J are the isotropic exchange coupling constants (J1 = J for an equilateral triangle) and G isthe antisymmetric exchange interaction vector.

We have performed CTM measurements on a 1.0 ˆ 0.5 ˆ 0.5 mm3 single crystal of V15 (Figure 3a).The torque signal is much weaker for V15 compared to Mn12 for similar crystal sizes. For a satisfactoryreproduction of CTM curves with a minimal model, it turns out that inclusion of the parametersg|| = 1.95, gK = 1.98, J1 = J = 0.847 cm´1 and G = (0, 0, 0) suffices [35]. Hence, g value anisotropyis sufficient to observe a nonzero magnetic torque signal and CTM does not help distinguishingbetween the two aforementioned scenarios. It must be noted here that the cantilever torquemeteris not calibrated and a quantitative measurement of the magnetic torque is therefore not possible.Frequency domain CD-TDESR spectra (Figure 3b) display a single clear resonance line for each appliedmagnetic field. This resonance line is attributed to the |S = 3/2, MS = ´3/2> to |3/2 ´1/2> transitionwith possible contributions from the |3/2 ´ 1/2> to |3/2 + 1/2>, |3/2 + 1/2> to |3/2 + 3/2>, and|1/2 ´ 1/2> to |1/2 + 1/2> transitions (Figure S2). The resonance line positions can be very wellaccounted for by spin Hamiltonian in Equation (2) with the same parameters used to reproduce CTMcurves. This demonstrates that anisotropy due to antisymmetric exchange interactions and/or g-valueanisotropy is enough for the successful measurement of TDESR spectra.

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a quantitative measurement of the magnetic torque is therefore not possible. Frequency domain CD‐

TDESR spectra (Figure 3b) display a single clear resonance line for each applied magnetic field. This 

resonance  line  is  attributed  to  the  |S  =  3/2, MS  =  −3/2>  to  |3/2  −1/2>  transition  with  possible 

contributions from the |3/2 − 1/2> to |3/2 + 1/2>, |3/2 + 1/2> to |3/2 + 3/2>, and |1/2 − 1/2> to |1/2 + 

1/2>  transitions  (Figure S2). The  resonance  line positions  can be very well accounted  for by  spin 

Hamiltonian  in  Equation  (2)  with  the  same  parameters  used  to  reproduce  CTM  curves.  This 

demonstrates that anisotropy due to antisymmetric exchange interactions and/or g‐value anisotropy 

is enough for the successful measurement of TDESR spectra. 

(a)  (b)

Figure 3. (a) capacitance as a function of angle for a single crystal of V15 at 7 K and different fields as 

indicated. Symbols represent experimental data while solid lines are calculated data; (b) frequency‐

domain CD‐TDESR spectra recorded on a single crystal of V15 with the field 2° from the unique crystal 

[1 1 1]‐axis, at 2 K and different fields as indicated. The solid and dashed lines are the measured and 

simulated spectra, respectively. 

In order to definitively clarify whether g‐value anisotropy alone allows successful measurement 

of TDESR spectra, we have expanded our investigation to the mononuclear copper(II) complex Cu‐

mnt. Here, the only possible source of magnetic anisotropy  is the g‐value anisotropy of the S = ½ 

copper(II) ion. Some of us have recently reported on the quantum coherent properties of this molecule 

[36]. A complication is that the compound crystallizes in a monoclinic space group, leading to two 

differently  oriented molecules  in  the  unit  cell  (Figure  S3). Reproduction  of CTM measurements 

(Figure 4a) thus requires summing up the contributions of the two molecules, each described by a 

spin Hamiltonian of the type: 

B B

B g S S A IH ,  (3)

where A accounts for the hyperfine interaction between the copper(II) unpaired electron and nuclear 

spins. Satisfactory simulations were obtained with g‖ = 2.0925 and g = 2.0227 (CTM curves are not 

sensitive to A) [36]. Figure 4b depicts CD‐TDESR spectra recorded on a 1.5 × 1.0 × 0.3 mm3 single 

crystal  of Cu‐mnt  at different  fields  and  angles. For  each  field/angle  combination,  a  single  clear 

resonance line is observed. The peak positions are well reproduced on the basis of Equation (3) with 

the same g‐values given above (Figure 4b). The shift of the resonance line due to the angle dependence 

of  the  effective  g  value  is  barely  resolved within  the  experimental  resolution.  In  addition,  the 

hyperfine coupling is not resolved. The field‐dependence of the resonance line intensity is due to the 

frequency dependence of the source intensity. 

Figure 3. (a) capacitance as a function of angle for a single crystal of V15 at 7 K and differentfields as indicated. Symbols represent experimental data while solid lines are calculated data;(b) frequency-domain CD-TDESR spectra recorded on a single crystal of V15 with the field 2˝ from theunique crystal [1 1 1]-axis, at 2 K and different fields as indicated. The solid and dashed lines are themeasured and simulated spectra, respectively.

In order to definitively clarify whether g-value anisotropy alone allows successful measurement ofTDESR spectra, we have expanded our investigation to the mononuclear copper(II) complex Cu-mnt.Here, the only possible source of magnetic anisotropy is the g-value anisotropy of the S = ½ copper(II)ion. Some of us have recently reported on the quantum coherent properties of this molecule [36].A complication is that the compound crystallizes in a monoclinic space group, leading to two differentlyoriented molecules in the unit cell (Figure S3). Reproduction of CTM measurements (Figure 4a) thusrequires summing up the contributions of the two molecules, each described by a spin Hamiltonian ofthe type:

H “ µBB ¨ g ¨ S` µBS ¨A ¨ I, (3)

Magnetochemistry 2016, 2, 25 6 of 9

where A accounts for the hyperfine interaction between the copper(II) unpaired electron and nuclearspins. Satisfactory simulations were obtained with g|| = 2.0925 and gK = 2.0227 (CTM curves arenot sensitive to A) [36]. Figure 4b depicts CD-TDESR spectra recorded on a 1.5 ˆ 1.0 ˆ 0.3 mm3

single crystal of Cu-mnt at different fields and angles. For each field/angle combination, a single clearresonance line is observed. The peak positions are well reproduced on the basis of Equation (3) withthe same g-values given above (Figure 4b). The shift of the resonance line due to the angle dependenceof the effective g value is barely resolved within the experimental resolution. In addition, the hyperfinecoupling is not resolved. The field-dependence of the resonance line intensity is due to the frequencydependence of the source intensity.Magnetochemistry 2016, 2, 25  6 of 8 

(a)  (b)

Figure 4. (a) capacitance as a function of angle for a single crystal of Cu‐mnt at 7 K and different fields 

as  indicated. The  upper  panel displays  the  individual  contributions  of  the  two molecules  in  the 

monoclinic unit cell; (b) capacitively detected frequency‐domain TDESR spectra recorded on a single 

crystal of Cu‐mnt at 2 K at different fields as indicated. Spectra are reported for different angles arising 

from different angles θ = 20° (light grey,  light green, orange), 30° (grey, green, red), and 40° (dark 

grey, olive, dark red). The upper graph shows the simulated electron spin resonance (ESR) absorption 

spectra with parameters given in the text. 

3. Discussion 

In the previous sections, we have demonstrated that essentially any type of magnetic anisotropy 

is sufficient to generate a finite magnetic torque signal, allowing the successful recording of TDESR 

spectra.  This  greatly  enhances  the  applicability  of  this  emerging  technique.  Optically  detected 

measurements employing a position‐sensitive detector did not strongly  improve sensitivity.  In  its 

current state, TDESR  is not  in a position to replace competing techniques, such as high‐frequency 

ESR, as the prime experimental method to determine magnetic anisotropies. We believe that this will 

remain so for bulk samples. We envision that OD‐TDESR may play a substantial role in investigating 

the  properties  of  oriented  thin  layers  of  magnetic  materials,  especially  when  implementing 

interferometric detection of the reflected laser beam inside the cryostat, thus eliminating the influence 

of relative vibrations of the detector with respect to the cryostat. 

4. Materials and Methods  

TDESR spectra were recorded by using a previously described home‐built spectrometer [20]. Fe4 

[37], Mn12 [38], V15 [39], and Cu‐mnt [36] were prepared as previously published. 

Supplementary Materials: The following are available online at www.mdpi.com/2312‐7481/2/2/25/s1, Figure S1: 

(a) Starting orientation for the cantilever torque magnetometry (CTM) measurement, indicating the crystal [0 0 1] (c‐

)axis and the direction of the external magnetic field B0; (b) Angle dependent CTM measurements recorded on a single 

crystal of Mn12 at 8 K and different fields as indicated. Figure S2: (a) Schematic picture of the spin structure of V15; 

(b) Starting orientation for the CTM measurement,  indicating the crystal (1 1 1) plane and the direction of the 

external magnetic field B0; (c) Qualitative energy level diagram  of V15 as a function of field. Figure S3: Starting 

orientation for the CTM measurement on Cu‐mnt, indicating the crystal b‐axis and the direction of the  external 

magnetic field B0. 

Acknowledgments:  We  thank  Deutsche  Forschungsgemeinschaft  DFG  (DR228/43‐1,  TRR21),  Fonds  der 

Chemischen  Industrie and  the Deutscher Akademischer Austauschdienst//Ministry of Education, Youth and 

Sports (DAAD/MEYS) grant 57154055 for funding. We thank Wolfgang Frey (Institut für Organische Chemie, 

Universität Stuttgart) for help with indexing the crystals. 

Author Contributions: Joris van Slageren, Lapo Bogani and Martin Dressel conceived the research, María Dörfel 

and Joris van Slageren designed the experiments, María Dörfel, Michal Kern, and Heiko Bamberger carried out 

all experimental work. María Dörfel analyzed all data, Joris van Slageren and Petr Neugebauer supervised all 

Figure 4. (a) capacitance as a function of angle for a single crystal of Cu-mnt at 7 K and differentfields as indicated. The upper panel displays the individual contributions of the two molecules in themonoclinic unit cell; (b) capacitively detected frequency-domain TDESR spectra recorded on a singlecrystal of Cu-mnt at 2 K at different fields as indicated. Spectra are reported for different angles arisingfrom different angles θ = 20˝ (light grey, light green, orange), 30˝ (grey, green, red), and 40˝ (darkgrey, olive, dark red). The upper graph shows the simulated electron spin resonance (ESR) absorptionspectra with parameters given in the text.

3. Discussion

In the previous sections, we have demonstrated that essentially any type of magnetic anisotropyis sufficient to generate a finite magnetic torque signal, allowing the successful recording of TDESRspectra. This greatly enhances the applicability of this emerging technique. Optically detectedmeasurements employing a position-sensitive detector did not strongly improve sensitivity. In itscurrent state, TDESR is not in a position to replace competing techniques, such as high-frequency ESR,as the prime experimental method to determine magnetic anisotropies. We believe that this will remainso for bulk samples. We envision that OD-TDESR may play a substantial role in investigating theproperties of oriented thin layers of magnetic materials, especially when implementing interferometricdetection of the reflected laser beam inside the cryostat, thus eliminating the influence of relativevibrations of the detector with respect to the cryostat.

4. Materials and Methods

TDESR spectra were recorded by using a previously described home-built spectrometer [20].Fe4 [37], Mn12 [38], V15 [39], and Cu-mnt [36] were prepared as previously published.

Magnetochemistry 2016, 2, 25 7 of 9

Supplementary Materials: The following are available online at www.mdpi.com/2312-7481/2/2/25/s1,Figure S1: (a) Starting orientation for the cantilever torque magnetometry (CTM) measurement, indicating thecrystal [0 0 1] (c-)axis and the direction of the external magnetic field B0; (b) Angle dependent CTM measurementsrecorded on a single crystal of Mn12 at 8 K and different fields as indicated. Figure S2: (a) Schematic picture ofthe spin structure of V15; (b) Starting orientation for the CTM measurement, indicating the crystal (1 1 1) planeand the direction of the external magnetic field B0; (c) Qualitative energy level diagram of V15 as a function offield. Figure S3: Starting orientation for the CTM measurement on Cu-mnt, indicating the crystal b-axis and thedirection of the external magnetic field B0.

Acknowledgments: We thank Deutsche Forschungsgemeinschaft DFG (DR228/43-1, TRR21), Fonds derChemischen Industrie and the Deutscher Akademischer Austauschdienst//Ministry of Education, Youth andSports (DAAD/MEYS) grant 57154055 for funding. We thank Wolfgang Frey (Institut für Organische Chemie,Universität Stuttgart) for help with indexing the crystals.

Author Contributions: Joris van Slageren, Lapo Bogani and Martin Dressel conceived the research, María Dörfeland Joris van Slageren designed the experiments, María Dörfel, Michal Kern, and Heiko Bamberger carriedout all experimental work. María Dörfel analyzed all data, Joris van Slageren and Petr Neugebauer supervisedall experimental work, Katharina Bader, Raphael Marx, Andrea Cornia, Tamoghna Mitra and Achim Müllersynthesized the samples, and María Dörfel and Joris van Slageren wrote the paper.

Conflicts of Interest: The authors declare no conflict of interest.

Abbreviations

The following abbreviations are used in this manuscript:

CTM Cantilever Torque MagnetometryTDESR Torque-Detected Electron Spin ResonanceCD Capacitively DetectedOD Optically DetectedHFESR High-Frequency Electron Spin ResonanceMNM Molecular NanoMagnetSQUID Superconducting Quantum Interference Device

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